Merging nurbs sphere with cylinder
Here's how I'd go about it:

Add your UV/Nurbs sphere.

Go into 'Edit Mode' and select the top faces then delete them like so:
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Go into edge mode and, whilst holding 'ALT' click the one next to it select the ring:
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Press 'E' then 'Z' to extrude that ring a little bit on the 'Z' axis
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Press CTRL+R to add about 3 loop cuts (scroll on mouse to increase number of cuts. For a sharper connection add 3 cuts or 4 depending on what you want.
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Using the 'Ring Select' method I described above, select the open ring and, again, extrude it up a little.
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Now add a SINGLE loop cut, as we did before, but this time, when you've done it, press CTRL+B to bevel it - using your scroll wheel to add 3 or 4 new edges.
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8.Move them up so that they're just below that top edge.
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Now select all of those top vertices and move them up to the desired height.
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Once again select that top open ring using the 'ALT' and click method.

Press 'F' to cap it.

Go into face select mode and select that new face.

Press I to inset that face by about 0.004, pretty much a tiny amount. You can change the values in the bottom left...
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Now add about 8 edge cuts, or as many as you need so that there are an even number of edges in-between the top and bottom of the cylinder.
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Come out of 'Edit Mode' right click you mesh and choose 'Shade Smooth'

Now add a 'Subsurface Modifier' and change the 'Levels Viewport' to 2 or 3 depending on what you'like.

You should now have this result: